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Journal of Function Spaces and Applications - Volume 6 2008, Issue 2, Pages 187-203

Dipartimento di Informatica, Università dell' Insubria, via Mazzini 5, 21100 Varese, Italy

Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma “La Sapienza”, via A. Scarpa 16, 00161 Rome, Italy

Received 1 July 2006

Academic Editor: Jürgen Appell

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this work we prove the existence of convolution on Marcinkiewicz spaces 𝔐pℝ, 1≤p<∞, and, using pointwise approximate identities, we extend the classical definition of Hilbert transform to such spaces.

Author: Federica Andreano and Renato Grande



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